Asymptotic expansion of the quasiconfluent hypergeometric function

Abstract

The asymptotic expansion of the hypergeometric function 2F1(a,b;c;z/b) in the case of quasiconfluence, i.e., for |b| → ∞, is revised. A very simple expansion, in terms of a semiasymptotic sequence of polynomials, is presented. Some properties of those polynomials are discussed. © 2003 American Institute of Physics.